Runaway avalanches in plasmas with external electric fields: spatially inhomogeneous case in a perturbation framework

TL;DR

This paper rigorously analyzes runaway electrons in plasmas under external electric fields, proving well-posedness and growth bounds for plasma velocity and temperature, and describing the asymptotic electron distribution.

Contribution

It introduces a novel coupled Landau-Coulomb system framework and establishes convergence to a Maxwellian distribution in a perturbative setting.

Findings

Mean velocity increases linearly over time.

Plasma temperature exhibits sharp logarithmic growth.

Electron distribution asymptotically approaches a scattering Maxwellian.

Abstract

We consider the Landau-Coulomb equation for a (hydrogen) plasma heated by an external electric field. In this setting, theoretical and experimental results in plasma physics show the emergence of so-called \emph{runaway electrons} which are linearly accelerating but only lead to a minimal increase of the plasma temperature. Runaway electrons are a major obstacle in nuclear fusion since they can overcome the confinement and damage the structure of the reactor. We rigorously prove the well-posedness of the underlying nonlinear \emph{open} Landau-Coulomb system in a perturbative setting and the conjectured growth bounds for the mean velocity and plasma temperature. We show that the mean velocity is linearly increasing in time, and capture the sharp logarithmic growth of the temperature. Furthermore, we prove that the electron distribution can be asymptotically described by a scattering-type Maxwellian. Due to the different nature of the electron-electron and electron-ion interactions, we recast the equation as a novel coupled system that allows us to isolate the dissipation structures of the two operators. For the coupled system, we perform a micro-macro decomposition to show convergence to the scattering-type Maxwellian.